Tilley, Burt S.
The purpose of this project was to mathematically model a Slinky-Coil Geothermal Heating System. We first consider and discuss the difficulties of modeling one loop of a slinky coil. We then reduce the problem further to analyzing a half-loop, through non-dimensionalization, separation of variables, eigenfunction expansions, and perturbation series to obtain a function to model the temperature of the slinky coil. In both cases, we examine the quasi-steady approximation, which gives us a steady-state solution to our problem. Our model can successfully model the temperature rise, but it is very inefficient as it requires a very large amount of loops, on the order of thousands, to sustain the ambient temperature of the soil.
Worcester Polytechnic Institute
Major Qualifying Project
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